The vast majority of the greatest scientific discoveries of all time have resulted directly from more powerful techniques for measuring light. Indeed, our most important source of information about our universe is light, and our ability to extract information from it is limited only by our ability to measure it.
Interestingly, most of the light in our universe remains immeasurable, involving long pulses of relatively broadband light, necessarily involving ultrafast and extremely complex temporal variations in their intensity and phase. As a result, it is important to develop techniques for measuring, ever more completely, light with ever more complex submicron detail in space and ever more complex ultrafast variations in time. The problem is severely complicated by the fact that the timescales involved correspond to the shortest events ever created, and measuring an event in time seems to require a shorter one, which, by definition, doesn't exist!
Nevertheless, we have developed simple, elegant techniques for completely measuring such light, using the light to measure itself and yielding a light pulse's intensity and phase vs. time and space. One technique involves making an optical spectrogram of the pulse using a nonlinear optical medium and whose mathematics is equivalent to the two-dimensional phase-retrieval problem—a problem that's solvable only because the Fundamental Theorem of Algebra fails for polynomials of two variables. In addition, we have recently developed simple methods for measuring the complete spatio-temporal electric field [E(x,y,z,t)] of an arbitrary, potentially complex light pulse without the need to average over multiple pulses.